Finite Group Databasebeta

← #13172657

Subgroups — #13172657

Order 1728.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#67C211yesmaximal, characteristic, complemented
2C2×#88953C211yesmaximal, characteristic, complemented
3#11723729C211yesmaximal, characteristic, complemented
4#11723629C211yesmaximal, characteristic, complemented
5#11723621C211yesmaximal, characteristic, complemented
6#11723615C211yesmaximal, characteristic, complemented
7C3×#63977C211yesmaximal, characteristic, complemented
8C3×#63971C211yesmaximal, characteristic, complemented
9#11722991C211yesmaximal, characteristic, complemented
10#11722988C211yesmaximal, characteristic, complemented
11#11722986C211yesmaximal, characteristic, complemented
12#11722956C211yesmaximal, characteristic, complemented
13#11722954C211yesmaximal, characteristic, complemented
14#11722951C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595524—31nomaximal
17#10595302—31nomaximal
18#10594263—31nomaximal
19C23×C32×D3C2211yescharacteristic, complemented
20C22×#1113C2211yescharacteristic, complemented
21C22×C3×D32C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×#6290C2211yescharacteristic
27C2×#6290C2211yescharacteristic, complemented
28C2×#6290C2211yescharacteristic, complemented
29C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
30C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
31C3×D3×#67—24no—
32C2×C3×#626C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#625C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38C2×C3×D3×Dic3C2211yescharacteristic, complemented
39#88953—24no—
40#88864C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88814C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52C3×#3724C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×C3×#67—31no—
57C2×C3×D3×D4—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×D3×#67D311yescharacteristic, complemented
61C2×#3802—31no—
62#64162—31no—
63#64148—31no—
64#64092—31no—
65C3×#953—31no—
66C3×#939—31no—
67C3×#884—31no—
68C3×#882—31no—
69#63983—31no—
70#63983—31no—
71#63983—31no—
72#63983—31no—
73#63980—31no—
74#63978—31no—
75#63977D311yescharacteristic, complemented
76#63976—31no—
77#63976—31no—
78#63976—61no—
79#63971—31no—
80#63971D311yescharacteristic, complemented
81#63970—31no—
82#63970—31no—
83#63970—31no—
84#63970—61no—
85#63969—31no—
86#63969—31no—
87#63969—31no—
88#63969—61no—
89D3×#217—31no—
90#63966—31no—
91#63961—31no—
92C2×(C2×D3)⋊Dic3—31no—
93#63922—31no—
94#63922—31no—
95D3×(C2×D3)⋊C4—31no—
96#63908—31no—
97#63905—31no—
98#63891—31no—
99#63885—31no—
100#63884—31no—
101#63884—31no—
102#63853—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3—22no—
109C22×C32×D3—41no—
110C22×C32×D3—41no—
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C22×C32×D3C2311yescharacteristic
114C2×#1113—22no—
115C2×#1113—41no—
116C2×#1113—41no—
117C2×C3×D32—41no—
118C2×C3×D32—41no—
119C2×C3×D32D414yescomplemented
120C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
121C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
122C3×#638—22no—
123C3×#638—41no—
124C3×#638—41no—
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C32×#67—22no—
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131C2×C32×Dic3C2311yescharacteristic
132#6290—22no—
133#6290—22no—
134#6290—41no—
135Dic3×C3⋊D3—22no—
136D3×C3⋊Dic3—41no—
137C3×#626—22no—
138C3×#626—22no—
139C3×#626—22no—
140C3×#626—41no—
141C3×#625—22no—
142C3×D3×Dic3—22no—
143C3×D3×Dic3—41no—
144#5804—91no—
145#5605—91no—
146#5589—91no—
147C24×C32—31no—
148C23×C3×D3—21no—
149C23×C3×D3—31no—
150C23×C3×D3—31no—
151C23×C3×D3C2×D311yescharacteristic, complemented
152C23×C3×D3C2×D311yescharacteristic, complemented
153C22×D32—31no—
154C22×D32—31no—
155C22×D32—31no—
156C22×D32C2×D311yescharacteristic
157C2×C32×D4—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638C2×D311yescharacteristic
162C2×#638C2×D311yescharacteristic, complemented
163C2×#638C2×D311yescharacteristic, complemented
164C22×C3⋊Dic3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—21no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—64no—
180C2×C3×#67—61no—
181C2×C3×#67—61no—
182C2×C3×#67—61no—
183C2×C3×#67C2×D311yescharacteristic, complemented
184C2×C3×#67C2×D311yescharacteristic, complemented
185C22×C3×Dic3—31no—
186C22×C3×Dic3—31no—
187C3×D3×D4—64no—
188C2×C3×D12—31no—
189C2×C3×D12—31no—
190C2×C3×D12—31no—
191C2×C3×D12—31no—
192C2×C3×C4×D3—31no—
193C2×C3×C4×D3—31no—
194D3×#67—24no—
195D3×#67—64no—
196D3×#67—64no—
197C2×#626C2×D311yescharacteristic
198C2×#626C2×D311yescharacteristic
199C2×#626C2×D311yescharacteristic, complemented
200C2×#626C2×D311yescharacteristic, complemented
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—31no—
204C2×#625—31no—
205C2×#625—31no—
206C2×#625—31no—
207C2×#625—61no—
208C2×#625—61no—
209C2×#625—61no—
210C2×#625C2×D311yescharacteristic, complemented
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—61no—
216C2×D3×Dic3—61no—
217C2×D3×Dic3C2×D311yescharacteristic, complemented
218C2×D3×Dic3C2×D311yescharacteristic, complemented
219#3802—64no—
220C32×C22⋊C4—31no—
221#3757—31no—
222#3757—31no—
223#3757—31no—
224#3757—31no—
225#3757—31no—
226#3757—61no—
227#3757—61no—
228#3757—61no—
229#3757—121no—
230#3752—31no—
231#3752—31no—
232C4⋊(C3⋊Dic3)—31no—
233#3750—31no—
234#3750—31no—
235C3×#217—21no—
236C3×#217—31no—
237C3×#217—31no—
238C3×#217C2×D311yescharacteristic, complemented
239C3×#217C2×D311yescharacteristic, complemented
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246#3724—31no—
247#3724—31no—
248#3724—61no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3—61no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722C2×D311yescharacteristic, complemented
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3—61no—
276(C2×D3)⋊Dic3—61no—
277(C2×D3)⋊Dic3—61no—
278(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
279(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2411yescharacteristic
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3C2×D412yes—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C2×C32×D3—21no—
300C2×C32×D3—44no—
301C2×C32×D3C2×D412yes—
302C2×C32×D3C2×D412yes—
303#1113—44no—
304C3×D32—44no—
305C3⋊(C3⋊Dic3)—21no—
306C3⋊(C3⋊Dic3)—21no—
307C3×C3⋊Dic3—21no—
308C3×C3⋊Dic3—21no—
309C3×C3⋊Dic3—21no—
310C32×Dic3—21no—
311C32×Dic3—21no—
312C32×Dic3—21no—
313C22×C3×D4—91no—
314C22×#67—31no—
315C22×#67—91no—
316C2×D3×D4—31no—
317C2×D3×D4—91no—
318C2×D3×D4—91no—
319C3×#121—91no—
320C3×#120—91no—
321#953—31no—
322#953—91no—
323#953—91no—
324#953—181no—
325C2×#217—91no—
326#939—31no—
327#939—91no—
328#939—91no—
329#939—91no—
330#939—91no—
331#939—91no—
332#939—181no—
333#938—91no—
334#938—91no—
335#937—91no—
336#937—91no—
337#937—91no—
338#937—91no—
339#937—91no—
340#937—91no—
341#935—91no—
342#935—91no—
343#935—91no—
344#930—91no—
345#929—91no—
346#929—91no—
347C2×(C2×D3)⋊C4—91no—
348#894—91no—
349#894—91no—
350#886—91no—
351#884—31no—
352#884—91no—
353#883—91no—
354#883—91no—
355#883—91no—
356#883—91no—
357#883—181no—
358#882—31no—
359#882—91no—
360D3×C22⋊C4—91no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—21no—
364C23×C32—31no—
365C23×C32—31no—
366C23×C32—31no—
367C23×C32—41no—
368C23×C32—62no—
369C23×C32—121no—
370C23×C32—121no—
371C23×C32C22×D311yescharacteristic
372C23×C32C22×D311yescharacteristic
373C23×C32C22×D311yescharacteristic
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3×D3—22no—
378C22×C3×D3—22no—
379C22×C3×D3—21no—
380C22×C3×D3—21no—
381C22×C3×D3—21no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—34no—
385C22×C3×D3—34no—
386C22×C3×D3—31no—
387C22×C3×D3—31no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—42no—
391C22×C3×D3—41no—
392C22×C3×D3—41no—
393C22×C3×D3—41no—
394C22×C3×D3—41no—
395C22×C3×D3—42no—
396C22×C3×D3—42no—
397C22×C3×D3—61no—
398C22×C3×D3—61no—
399C22×C3×D3—61no—
400C22×C3×D3—121no—
401C22×C3×D3—121no—
402C22×C3×D3—121no—
403C22×C3×D3—121no—
404C22×C3×D3C22×D311yescharacteristic
405C22×C3×D3C22×D311yescharacteristic
406C22×C3×D3C22×D311yescharacteristic
407C22×C3×D3C22×D311yescharacteristic
408C22×C3×D3C22×D311yescharacteristic
409C22×C3×D3C22×D311yescharacteristic
410C2×D32—41no—
411C2×D32—41no—
412C2×D32—62no—
413C2×D32—62no—
414C2×D32—62no—
415C2×D32—121no—
416C2×D32—121no—
417C2×D32—121no—
418C2×D32—121no—
419C2×D32—121no—
420C2×D32—121no—
421C2×D32#6714yescomplemented
422C32×D4—62no—
423C2×C32×C4—31no—
424C2×C32×C4—31no—
425C2×C32×C4—31no—
426#638—22no—
427#638—41no—
428#638—41no—
429#638—62no—
430#638—62no—
431#638—121no—
432C2×C3⋊Dic3—31no—
433C2×C3⋊Dic3—31no—
434C2×C3⋊Dic3—31no—
435C2×C3⋊Dic3—31no—
436C2×C3⋊Dic3—31no—
437C2×C3⋊Dic3—31no—
438C2×C3⋊Dic3—61no—
439C2×C3⋊Dic3—61no—
440C2×C3⋊Dic3—61no—
441C2×C3⋊Dic3—61no—
442C2×C3⋊Dic3—61no—
443C2×C3⋊Dic3—61no—
444C2×C3⋊Dic3—121no—
445C2×C3⋊Dic3—121no—
446C2×C3⋊Dic3—121no—
447C2×C3⋊Dic3C22×D311yescharacteristic
448C2×C3⋊Dic3C22×D311yescharacteristic
449C2×C3⋊Dic3C22×D311yescharacteristic
450C4×C3⋊D3—62no—
451C3×#67—22no—
452C3×#67—22no—
453C3×#67—42no—
454C3×#67—62no—
455C3×#67—62no—
456C3×#67—62no—
457C3×#67—62no—
458C3×#67—62no—
459C3×#67—62no—
460C3×#67—62no—
461C3×#67—122no—
462C3×#67—121no—
463C3×#67—121no—
464C3×#67—121no—
465C3×#67—121no—
466C3×#67—121no—
467C3×#67—122no—
468C3×#67—122no—
469C2×C3×Dic3—21no—
470C2×C3×Dic3—21no—
471C2×C3×Dic3—21no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—31no—
475C2×C3×Dic3—31no—
476C2×C3×Dic3—31no—
477C2×C3×Dic3—31no—
478C2×C3×Dic3—61no—
479C2×C3×Dic3—61no—
480C2×C3×Dic3—61no—
481C2×C3×Dic3—62no—
482C2×C3×Dic3—121no—
483C2×C3×Dic3C22×D311yescharacteristic
484C2×C3×Dic3C22×D311yescharacteristic
485C2×C3×Dic3C22×D311yescharacteristic
486C2×C3×Dic3C22×D311yescharacteristic
487C2×C3×Dic3C22×D311yescharacteristic
488C2×C3×Dic3C22×D311yescharacteristic
489C3×D12—62no—
490C3×D12—62no—
491C3×D12—62no—
492C3×D12—121no—
493C3×C4×D3—62no—
494C3×C4×D3—121no—
495#626—22no—
496#626—22no—
497#626—22no—
498#626—41no—
499#625—22no—
500#625—62no—
501#625—62no—
502#625—62no—
503#625—62no—
504#625—122no—
505#625—122no—
506#625—121no—
507#625—121no—
508#625—122no—
509D3×Dic3—22no—
510D3×Dic3—41no—
511D3×Dic3—62no—
512D3×Dic3—62no—
513D3×Dic3—122no—
514D3×Dic3—121no—
515D3×Dic3—121no—
516D3×Dic3—122no—
517#534—271noSylow
518C2×C33—41no—
519C2×C33C22×D411yescharacteristic
520C2×C33H(5,𝔽2)11yescharacteristic
521C2×C33H(5,𝔽2)11yescharacteristic
522C3×C3⋊D3—22no—
523C3×C3⋊D3—41no—
524C3×C3⋊D3—41no—
525C32×D3—22no—
526C32×D3—22no—
527C32×D3—41no—
528C24×C3—31no—
529C24×C3—31no—
530C24×C3—61no—
531C24×C3—91no—
532C23×D3—31no—
533C23×D3—31no—
534C23×D3—91no—
535C23×D3—91no—
536C23×D3—91no—
537C23×D3D3211yescharacteristic, complemented
538C2×C3×D4—31no—
539C2×C3×D4—31no—
540C2×C3×D4—61no—
541C2×C3×D4—91no—
542C2×C3×D4—91no—
543C2×C3×D4—91no—
544C2×C3×D4—91no—
545C2×C3×D4—91no—
546C2×C3×D4—91no—
547C2×C3×D4—91no—
548C2×C3×D4—91no—
549C2×C3×D4—184no—
550C22×C3×C4—91no—
551C22×C3×C4—91no—
552C2×#67—31no—
553C2×#67—31no—
554C2×#67—31no—
555C2×#67—31no—
556C2×#67—31no—
557C2×#67—31no—
558C2×#67—31no—
559C2×#67—31no—
560C2×#67—31no—
561C2×#67—31no—
562C2×#67—31no—
563C2×#67—31no—
564C2×#67—61no—
565C2×#67—61no—
566C2×#67—61no—
567C2×#67—64no—
568C2×#67—91no—
569C2×#67—91no—
570C2×#67—91no—
571C2×#67—91no—
572C2×#67—91no—
573C2×#67—91no—
574C2×#67—91no—
575C2×#67—91no—
576C2×#67—91no—
577C2×#67—181no—
578C2×#67—181no—
579C2×#67—181no—
580C2×#67—184no—
581C2×#67D3211yescharacteristic, complemented
582C22×Dic3—31no—
583C22×Dic3—31no—
584C22×Dic3—91no—
585C22×Dic3—91no—
586C22×Dic3—91no—
587C22×Dic3—181no—
588D3×D4—64no—
589D3×D4—184no—
590D3×D4—184no—
591C2×D12—31no—
592C2×D12—31no—
593C2×D12—31no—
594C2×D12—31no—
595C2×C4×D3—31no—
596C2×C4×D3—31no—
597C2×C4×D3—91no—
598C2×C4×D3—91no—
599C2×C4×D3—91no—
600C2×C4×D3—181no—
601C3×C4⋊C4—91no—
602C3×C22⋊C4—31no—
603C3×C22⋊C4—31no—
604C3×C22⋊C4—61no—
605C3×C22⋊C4—91no—
606C3×C22⋊C4—91no—
607C3×C22⋊C4—91no—
608#217—31no—
609#217—31no—
610#217—91no—
611#217—91no—
612#217—91no—
613#217—91no—
614#217—91no—
615#217—91no—
616#217—91no—
617#217—91no—
618#217—91no—
619#217—91no—
620#217—91no—
621#217—91no—
622#217—181no—
623#217—181no—
624#217—181no—
625#217—181no—
626#217—181no—
627#217—361no—
628#217D3211yescharacteristic, complemented
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—31no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—31no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—181no—
646(C2×D3)⋊C4—181no—
647C4⋊Dic3—91no—
648C4⋊Dic3—91no—
649C4⋊Dic3—91no—
650C4⋊Dic3—181no—
651Dic3⋊C4—31no—
652Dic3⋊C4—31no—
653Dic3⋊C4—91no—
654Dic3⋊C4—91no—
655Dic3⋊C4—91no—
656Dic3⋊C4—91no—
657Dic3⋊C4—91no—
658Dic3⋊C4—91no—
659Dic3⋊C4—181no—
660Dic3⋊C4—181no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—32no—
675C22×C32—32no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—42no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—61no—
687C22×C32—61no—
688C22×C32—61no—
689C22×C32—61no—
690C22×C32—61no—
691C22×C32—61no—
692C22×C32—61no—
693C22×C32—81no—
694C22×C32—81no—
695C22×C32—124no—
696C22×C32C23×D311yescharacteristic
697C22×C32C23×D311yescharacteristic
698C22×C32C23×D311yescharacteristic
699C2×C3⋊D3—21no—
700C2×C3⋊D3—21no—
701C2×C3⋊D3—21no—
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—21no—
705C2×C3⋊D3—21no—
706C2×C3⋊D3—21no—
707C2×C3⋊D3C2×#6712yes—
708C2×C3×D3—21no—
709C2×C3×D3—21no—
710C2×C3×D3—21no—
711C2×C3×D3—21no—
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—21no—
716C2×C3×D3—22no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—21no—
723C2×C3×D3—22no—
724C2×C3×D3—22no—
725C2×C3×D3—32no—
726C2×C3×D3—32no—
727C2×C3×D3—41no—
728C2×C3×D3—41no—
729C2×C3×D3—41no—
730C2×C3×D3—41no—
731C2×C3×D3—41no—
732C2×C3×D3—41no—
733C2×C3×D3—44no—
734C2×C3×D3—44no—
735C2×C3×D3—48no—
736C2×C3×D3—62no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—61no—
748C2×C3×D3—61no—
749C2×C3×D3—61no—
750C2×C3×D3—61no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—121no—
754C2×C3×D3—121no—
755C2×C3×D3—121no—
756C2×C3×D3—121no—
757C2×C3×D3—121no—
758C2×C3×D3—121no—
759C2×C3×D3—121no—
760C2×C3×D3—121no—
761C2×C3×D3—124no—
762C2×C3×D3—124no—
763C2×C3×D3D3×D412yes—
764C2×C3×D3D3×D412yes—
765C2×C3×D3C2×#6712yes—
766C2×C3×D3C2×#6712yes—
767D32—44no—
768D32—124no—
769D32—124no—
770D32—124no—
771C32×C4—61no—
772C32×C4—61no—
773C32×C4—61no—
774C3⋊Dic3—21no—
775C3⋊Dic3—21no—
776C3⋊Dic3—21no—
777C3⋊Dic3—61no—
778C3⋊Dic3—61no—
779C3⋊Dic3—61no—
780C3⋊Dic3—61no—
781C3⋊Dic3—61no—
782C3⋊Dic3—61no—
783C3⋊Dic3—121no—
784C3⋊Dic3—121no—
785C3⋊Dic3—121no—
786C3⋊Dic3—121no—
787C3⋊Dic3—121no—
788C3⋊Dic3—121no—
789C3⋊Dic3—241no—
790C3⋊Dic3—241no—
791C3×Dic3—21no—
792C3×Dic3—21no—
793C3×Dic3—21no—
794C3×Dic3—21no—
795C3×Dic3—21no—
796C3×Dic3—21no—
797C3×Dic3—41no—
798C3×Dic3—41no—
799C3×Dic3—41no—
800C3×Dic3—62no—
801C3×Dic3—61no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—121no—
808C3×Dic3—121no—
809C22×D4—91no—
810C22×D4—271no—
811#123—271no—
812#123—271no—
813#123—271no—
814#123—271no—
815#121—91no—
816#121—271no—
817#121—271no—
818#121—271no—
819#120—91no—
820#120—271no—
821#120—271no—
822#120—271no—
823C2×C22⋊C4—271no—
824C33#53411yescharacteristic, complemented, Sylow
825C23×C3—21no—
826C23×C3—21no—
827C23×C3—21no—
828C23×C3—31no—
829C23×C3—31no—
830C23×C3—31no—
831C23×C3—31no—
832C23×C3—31no—
833C23×C3—31no—
834C23×C3—41no—
835C23×C3—61no—
836C23×C3—61no—
837C23×C3—61no—
838C23×C3—62no—
839C23×C3—62no—
840C23×C3—94no—
841C23×C3—91no—
842C23×C3—91no—
843C23×C3—91no—
844C23×C3—122no—
845C23×C3—121no—
846C23×C3—121no—
847C23×C3—121no—
848C23×C3—121no—
849C23×C3—122no—
850C23×C3—122no—
851C23×C3—361no—
852C23×C3—361no—
853C23×C3C2×D3211yescharacteristic
854C23×C3C2×D3211yescharacteristic
855C23×C3C2×D3211yescharacteristic
856C22×D3—22no—
857C22×D3—31no—
858C22×D3—31no—
859C22×D3—34no—
860C22×D3—34no—
861C22×D3—31no—
862C22×D3—31no—
863C22×D3—31no—
864C22×D3—31no—
865C22×D3—41no—
866C22×D3—41no—
867C22×D3—61no—
868C22×D3—61no—
869C22×D3—61no—
870C22×D3—121no—
871C22×D3—121no—
872C22×D3—121no—
873C22×D3—121no—
874C22×D3—182no—
875C22×D3—182no—
876C22×D3—182no—
877C22×D3—361no—
878C22×D3—361no—
879C22×D3—361no—
880C22×D3—361no—
881C22×D3—361no—
882C22×D3—361no—
883C22×D3C2×D3211yescharacteristic
884C22×D3C2×D3211yescharacteristic
885C22×D3C2×D3211yescharacteristic
886C3×D4—62no—
887C3×D4—62no—
888C3×D4—122no—
889C3×D4—182no—
890C3×D4—182no—
891C3×D4—182no—
892C3×D4—182no—
893C3×D4—182no—
894C3×D4—361no—
895C3×D4—361no—
896C3×D4—361no—
897C2×C3×C4—31no—
898C2×C3×C4—31no—
899C2×C3×C4—31no—
900C2×C3×C4—31no—
901C2×C3×C4—31no—
902C2×C3×C4—31no—
903C2×C3×C4—61no—
904C2×C3×C4—61no—
905C2×C3×C4—61no—
906C2×C3×C4—91no—
907C2×C3×C4—91no—
908C2×C3×C4—91no—
909C2×C3×C4—182no—
910C2×C3×C4—361no—
911#67—22no—
912#67—62no—
913#67—62no—
914#67—62no—
915#67—62no—
916#67—62no—
917#67—62no—
918#67—62no—
919#67—122no—
920#67—121no—
921#67—121no—
922#67—121no—
923#67—121no—
924#67—121no—
925#67—122no—
926#67—122no—
927#67—182no—
928#67—182no—
929#67—182no—
930#67—182no—
931#67—182no—
932#67—182no—
933#67—362no—
934#67—362no—
935#67—361no—
936#67—361no—
937#67—361no—
938#67—362no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—31no—
945C2×Dic3—61no—
946C2×Dic3—61no—
947C2×Dic3—61no—
948C2×Dic3—62no—
949C2×Dic3—91no—
950C2×Dic3—91no—
951C2×Dic3—91no—
952C2×Dic3—91no—
953C2×Dic3—91no—
954C2×Dic3—91no—
955C2×Dic3—121no—
956C2×Dic3—181no—
957C2×Dic3—181no—
958C2×Dic3—181no—
959C2×Dic3—181no—
960C2×Dic3—181no—
961C2×Dic3—181no—
962C2×Dic3—182no—
963C2×Dic3—361no—
964C2×Dic3—361no—
965C2×Dic3—361no—
966C2×Dic3—361no—
967C2×Dic3—362no—
968C2×Dic3C2×D3211yescharacteristic
969C2×Dic3C2×D3211yescharacteristic
970C2×Dic3C2×D3211yescharacteristic
971D12—62no—
972D12—62no—
973D12—62no—
974D12—121no—
975C4×D3—62no—
976C4×D3—121no—
977C4×D3—182no—
978C4×D3—182no—
979C4×D3—362no—
980C4×D3—361no—
981C2×C32—21no—
982C2×C32—21no—
983C2×C32—21no—
984C2×C32—21no—
985C2×C32—21no—
986C2×C32—21no—
987C2×C32—21no—
988C2×C32—21no—
989C2×C32—21no—
990C2×C32—41no—
991C2×C32—41no—
992C2×C32—41no—
993C2×C32—41no—
994C2×C32—42no—
995C2×C32—41no—
996C2×C32—41no—
997C2×C32—62no—
998C2×C32—62no—
999C2×C32—81no—
1000C2×C32—81no—
1001C2×C32—82no—
1002C2×C32—121no—
1003C2×C32C2×D3×D411yescharacteristic
1004C2×C32C2×D3×D411yescharacteristic
1005C2×C32#100411yescharacteristic
1006C2×C32#100411yescharacteristic
1007C2×C32#100411yescharacteristic
1008C2×C32#100411yescharacteristic
1009C2×C32#100411yescharacteristic
1010C2×C32#100911yescharacteristic
1011C2×C32C22×#6711yescharacteristic
1012C3⋊D3—22no—
1013C3⋊D3—41no—
1014C3⋊D3—41no—
1015C3×D3—22no—
1016C3×D3—22no—
1017C3×D3—22no—
1018C3×D3—22no—
1019C3×D3—42no—
1020C3×D3—42no—
1021C3×D3—42no—
1022C3×D3—41no—
1023C3×D3—41no—
1024C3×D3—62no—
1025C3×D3—62no—
1026C3×D3—122no—
1027C3×D3—121no—
1028C3×D3—121no—
1029C3×D3—121no—
1030C3×D3—121no—
1031C3×D3—241no—
1032C3×D3—241no—
1033C24—31no—
1034C24—91no—
1035C24—271no—
1036C2×D4—31no—
1037C2×D4—91no—
1038C2×D4—91no—
1039C2×D4—91no—
1040C2×D4—91no—
1041C2×D4—91no—
1042C2×D4—91no—
1043C2×D4—91no—
1044C2×D4—91no—
1045C2×D4—184no—
1046C2×D4—271no—
1047C2×D4—271no—
1048C2×D4—271no—
1049C2×D4—544no—
1050C22×C4—91no—
1051C22×C4—91no—
1052C22×C4—271no—
1053C22×C4—271no—
1054C4⋊C4—91no—
1055C4⋊C4—271no—
1056C4⋊C4—271no—
1057C4⋊C4—271no—
1058C22⋊C4—31no—
1059C22⋊C4—91no—
1060C22⋊C4—91no—
1061C22⋊C4—91no—
1062C22⋊C4—271no—
1063C22⋊C4—271no—
1064C22⋊C4—271no—
1065C22⋊C4—271no—
1066C22⋊C4—271no—
1067C22⋊C4—271no—
1068C22⋊C4—271no—
1069C22⋊C4—271no—
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—21no—
1073C22×C3—21no—
1074C22×C3—21no—
1075C22×C3—21no—
1076C22×C3—21no—
1077C22×C3—21no—
1078C22×C3—21no—
1079C22×C3—21no—
1080C22×C3—21no—
1081C22×C3—21no—
1082C22×C3—21no—
1083C22×C3—32no—
1084C22×C3—32no—
1085C22×C3—32no—
1086C22×C3—32no—
1087C22×C3—41no—
1088C22×C3—41no—
1089C22×C3—41no—
1090C22×C3—41no—
1091C22×C3—41no—
1092C22×C3—41no—
1093C22×C3—41no—
1094C22×C3—41no—
1095C22×C3—42no—
1096C22×C3—41no—
1097C22×C3—62no—
1098C22×C3—62no—
1099C22×C3—62no—
1100C22×C3—61no—
1101C22×C3—61no—
1102C22×C3—61no—
1103C22×C3—61no—
1104C22×C3—61no—
1105C22×C3—61no—
1106C22×C3—61no—
1107C22×C3—61no—
1108C22×C3—61no—
1109C22×C3—61no—
1110C22×C3—61no—
1111C22×C3—61no—
1112C22×C3—61no—
1113C22×C3—61no—
1114C22×C3—81no—
1115C22×C3—81no—
1116C22×C3—92no—
1117C22×C3—121no—
1118C22×C3—121no—
1119C22×C3—121no—
1120C22×C3—121no—
1121C22×C3—121no—
1122C22×C3—121no—
1123C22×C3—124no—
1124C22×C3—124no—
1125C22×C3—128no—
1126C22×C3—181no—
1127C22×C3—181no—
1128C22×C3—181no—
1129C22×C3—181no—
1130C22×C3—181no—
1131C22×C3—181no—
1132C22×C3—181no—
1133C22×C3—181no—
1134C22×C3—364no—
1135C22×C3C22×D3211yescharacteristic
1136C22×C3C22×D3211yescharacteristic
1137C22×C3C22×D3211yescharacteristic
1138C2×D3—21no—
1139C2×D3—21no—
1140C2×D3—21no—
1141C2×D3—21no—
1142C2×D3—21no—
1143C2×D3—21no—
1144C2×D3—21no—
1145C2×D3—32no—
1146C2×D3—32no—
1147C2×D3—44no—
1148C2×D3—62no—
1149C2×D3—61no—
1150C2×D3—61no—
1151C2×D3—61no—
1152C2×D3—61no—
1153C2×D3—61no—
1154C2×D3—61no—
1155C2×D3—61no—
1156C2×D3—61no—
1157C2×D3—61no—
1158C2×D3—61no—
1159C2×D3—61no—
1160C2×D3—61no—
1161C2×D3—61no—
1162C2×D3—61no—
1163C2×D3—61no—
1164C2×D3—61no—
1165C2×D3—121no—
1166C2×D3—121no—
1167C2×D3—121no—
1168C2×D3—121no—
1169C2×D3—121no—
1170C2×D3—121no—
1171C2×D3—121no—
1172C2×D3—121no—
1173C2×D3—124no—
1174C2×D3—124no—
1175C2×D3—364no—
1176C2×D3—364no—
1177C2×D3—364no—
1178C2×D3D3×#6712yes—
1179C2×D3D3×#6712yes—
1180C3×C4—61no—
1181C3×C4—61no—
1182C3×C4—61no—
1183C3×C4—61no—
1184C3×C4—61no—
1185C3×C4—61no—
1186C3×C4—121no—
1187C3×C4—121no—
1188C3×C4—121no—
1189C3×C4—181no—
1190C3×C4—181no—
1191C3×C4—181no—
1192Dic3—21no—
1193Dic3—21no—
1194Dic3—21no—
1195Dic3—62no—
1196Dic3—61no—
1197Dic3—61no—
1198Dic3—61no—
1199Dic3—61no—
1200Dic3—61no—
1201Dic3—61no—
1202Dic3—121no—
1203Dic3—121no—
1204Dic3—181no—
1205Dic3—181no—
1206Dic3—181no—
1207Dic3—181no—
1208Dic3—181no—
1209Dic3—181no—
1210Dic3—361no—
1211Dic3—361no—
1212Dic3—361no—
1213Dic3—361no—
1214Dic3—361no—
1215Dic3—361no—
1216Dic3—721no—
1217Dic3—721no—
1218C32—21no—
1219C32—21no—
1220C32—21no—
1221C32—41no—
1222C32#558911yescharacteristic, complemented
1223C32#560511yescharacteristic, complemented
1224C32#580411yescharacteristic, complemented
1225C23—31no—
1226C23—31no—
1227C23—31no—
1228C23—62no—
1229C23—94no—
1230C23—91no—
1231C23—91no—
1232C23—91no—
1233C23—121no—
1234C23—121no—
1235C23—361no—
1236C23—361no—
1237C23—542no—
1238C23—1081no—
1239C23—1081no—
1240C23D3311yescharacteristic
1241D4—62no—
1242D4—182no—
1243D4—182no—
1244D4—182no—
1245D4—182no—
1246D4—182no—
1247D4—361no—
1248D4—361no—
1249D4—361no—
1250D4—542no—
1251D4—542no—
1252D4—1081no—
1253C2×C4—31no—
1254C2×C4—31no—
1255C2×C4—31no—
1256C2×C4—91no—
1257C2×C4—91no—
1258C2×C4—91no—
1259C2×C4—182no—
1260C2×C4—271no—
1261C2×C4—271no—
1262C2×C4—361no—
1263C2×C4—542no—
1264C2×C4—1081no—
1265C2×C3—21no—
1266C2×C3—21no—
1267C2×C3—21no—
1268C2×C3—21no—
1269C2×C3—21no—
1270C2×C3—21no—
1271C2×C3—21no—
1272C2×C3—21no—
1273C2×C3—21no—
1274C2×C3—42no—
1275C2×C3—41no—
1276C2×C3—41no—
1277C2×C3—41no—
1278C2×C3—41no—
1279C2×C3—41no—
1280C2×C3—41no—
1281C2×C3—62no—
1282C2×C3—62no—
1283C2×C3—62no—
1284C2×C3—62no—
1285C2×C3—81no—
1286C2×C3—81no—
1287C2×C3—82no—
1288C2×C3—122no—
1289C2×C3—122no—
1290C2×C3—122no—
1291C2×C3—121no—
1292C2×C3—121no—
1293C2×C3—182no—
1294C2×C3—361no—
1295C2×C3—361no—
1296C2×C3#6430711yescharacteristic
1297C2×C3D32×D411yescharacteristic
1298C2×C3#6431311yescharacteristic
1299C2×C3#6431311yescharacteristic
1300C2×C3#6431411yescharacteristic
1301C2×C3C2×D3×#6711yescharacteristic
1302C2×C3C2×D3×#6711yescharacteristic
1303C2×C3#6433011yescharacteristic
1304C2×C3#6433011yescharacteristic
1305D3—22no—
1306D3—22no—
1307D3—41no—
1308D3—62no—
1309D3—62no—
1310D3—122no—
1311D3—121no—
1312D3—121no—
1313D3—121no—
1314D3—121no—
1315D3—241no—
1316D3—241no—
1317C22—21no—
1318C22—21no—
1319C22—21no—
1320C22—32no—
1321C22—32no—
1322C22—61no—
1323C22—61no—
1324C22—61no—
1325C22—61no—
1326C22—61no—
1327C22—61no—
1328C22—61no—
1329C22—92no—
1330C22—124no—
1331C22—181no—
1332C22—181no—
1333C22—181no—
1334C22—181no—
1335C22—181no—
1336C22—181no—
1337C22—181no—
1338C22—181no—
1339C22—364no—
1340C22—1084no—
1341C22C2×D3311yescharacteristic
1342C4—61no—
1343C4—61no—
1344C4—61no—
1345C4—181no—
1346C4—181no—
1347C4—181no—
1348C4—541no—
1349C4—541no—
1350C3—21no—
1351C3—21no—
1352C3—21no—
1353C3—41no—
1354C3#1059426311yescharacteristic, complemented
1355C3#1059530211yescharacteristic, complemented
1356C3#1059552411yescharacteristic, complemented
1357C2—41no—
1358C2—62no—
1359C2—62no—
1360C2—121no—
1361C2—182no—
1362C2—361no—
1363C2—361no—
1364C2#1172441511yescharacteristic
1365C2#1172441811yescharacteristic
1366C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×D3×#67C2semidirect
2. C2×#88953C2semidirect
3. #11723729C2semidirect
4. #11723629C2semidirect
5. #11723621C2semidirect
6. #11723615C2semidirect
7. C3×#63977C2semidirect
8. C3×#63971C2semidirect
9. #11722991C2semidirect
10. #11722988C2semidirect
11. #11722986C2semidirect
12. #11722956C2semidirect
13. #11722954C2semidirect
14. #11722951C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
19. C23×C32×D3C22semidirect
20. C22×#1113C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
27. C2×#6290C22semidirect
28. C2×#6290C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
30. C2×D3×C3⋊Dic3C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#625C22semidirect
37. C2×C3×D3×Dic3C22semidirect
38. C2×C3×D3×Dic3C22semidirect
40. #88864C22semidirect
41. C32×#217C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88814C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88803C22semidirect
49. #88803C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. C3×#3724C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
60. C2×D3×#67D3semidirect
75. #63977D3semidirect
80. #63971D3semidirect
119. C2×C3×D32D4semidirect
151. C23×C3×D3C2×D3semidirect
152. C23×C3×D3C2×D3semidirect
162. C2×#638C2×D3semidirect
163. C2×#638C2×D3semidirect
183. C2×C3×#67C2×D3semidirect
184. C2×C3×#67C2×D3semidirect
199. C2×#626C2×D3semidirect
200. C2×#626C2×D3semidirect
210. C2×#625C2×D3semidirect
217. C2×D3×Dic3C2×D3semidirect
218. C2×D3×Dic3C2×D3semidirect
238. C3×#217C2×D3semidirect
239. C3×#217C2×D3semidirect
249. #3724C2×D3semidirect
259. #3722C2×D3semidirect
278. (C2×D3)⋊Dic3C2×D3semidirect
279. (C2×D3)⋊Dic3C2×D3semidirect
421. C2×D32#67semidirect
537. C23×D3D32semidirect
581. C2×#67D32semidirect
628. #217D32semidirect
824. C33#534semidirect
1222. C32#5589semidirect
1223. C32#5605semidirect
1224. C32#5804semidirect
1354. C3#10594263semidirect
1355. C3#10595302semidirect
1356. C3#10595524semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×D3×#672
C2×#889532
#117237292
#117236292
#117236212
#117236152
C3×#639772
C3×#639712
#117229912
#117229882
#117229862
#117229562
#117229542
#117229512
D3×(C2×D3)⋊Dic32
#105955243
#105953023
#105942633